A non-homogeneous negative binomial autoregressive model for forecasting port truck arrivals

Accurate forecasting of daily truck arrivals is crucial for optimizing port logistics operations. Truck arrivals are typically modeled as a counting process exhibiting two complex features: serial correlation and nonstationarity. Autoregressive models are commonly employed to address serial correlation, but they often assume stationarity, which limits their ability to capture non-stationary dynamics. Conversely, the non-homogeneous Poisson process is commonly used to model non-stationarity in arrival processes. Yet it fails to account for serial correlation and is insufficient to capture the overdispersion frequently observed in real-world counting processes. To overcome these limitations, we propose a novel forecasting model that integrates an autoregressive framework with a non-homogeneous negative binomial distribution to model daily truck arrivals, capturing serial autocorrelation, nonstationarity, and overdispersion. The proposed approach generates predictions using an autoregressive model, which are then transformed into realizations of the non-homogeneous negative binomial distribution via the inverse transform method. Based on real-world daily truck arrival data at a major Chilean port, the proposed model is evaluated against established benchmark models. The results show that the proposed model achieves competitive point-forecast accuracy while providing substantially more informative and better-calibrated predictive distributions, particularly in terms of prediction-interval sharpness and coverage balance. The broader implications for modeling and practical management are also discussed.